Class25 - Amggmg $13 ._ h _.. m n. __ m _ § {9 Wabbit...

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Unformatted text preview: Amggmg $13 ._ h _.. m n. __ m _ § {9 Wabbit Rama-e; '. bah > A; = web; ' “33‘ Mam §£aggwgafi ,1 _ b8am¥k nggwnow) (\fifiammk r (“M Jiggggfiw gimgfm Qafizn) h aficw gg émmwfi fimfi égs-aé Hmfi __ V; Lt) = 2 Vi,“ ALGA 5'! gs “$"Efif’séf gigwgaaaa 96 H0153; ) Li DUE; “Tb Lam Wswaw 3;, s A LL17) is $956.07» Accepgg anew 74L=LJLEL BMW m fie mg _. mm 3 Vi; A; M =V3‘x.. 3435?: fi'ffi? gawflazam flaw wwmsggz gfimu Response spectrum for El Centro ground motion 0, and 20%. Pseudo-vetocity V, in./sec J Natural vibration period Tn, see Figure 5.641er Dynamics of Structures: Theory and Applications to Earthquake Engineering, by Anil K. Chopra, Prentice-Halt, 2001. iii? $§“?$€EY@ Wait-$2 70$ E’EMMETS 22413:}: $353 22,-? [$1 Eng?) ‘ fig LC}: 8J7} flab; 2/115:qu Vac; fflfiwé if: Q gfifiafi P if it; @Mm m “fizgfifigm Wagg. - 5' wAvg m Qafififigfiifi Mmaem I (E? AESaLééfi- $5M fygwfii : Z [VLJMékfiI 5/517 4 ~———.. Kama ‘ Paak Easgrfigw figgwwmg 25?} asgm? a???“ “%“%“’w%_w ...%€gmagwmgfi. Mats; . : him ~ Afl’gmca we r165 92w? {,4wa Wim Qfa. wag” (Mam. fififififia a%_ ma?” {:éfi‘frfiififfifj 69 Comm @QAfifiwgffiéfl Cawfiéfififiméfiéé QC ) EULfi‘, MW 62. éfirrafiai‘iw (baggageng éérfix-gfim 2‘ ...__ .. _ wag—ummuumwlwmmm. 224m 5:) sagas 22142 1023 swam 22-144 299 SHEETS @flmfimm fl. ; 5i 0&3): *4 ififig, (ma-g“) id; w gfifyéfé 5e}??? 5K3?) [L0 350%{3 (mg 55; WWWa I hi: i :l {w g.‘ ¥ 1.63 v” (Mn/M W014: €14 Correlation coefficient Correlation coeffcient pin 0.6 0.7 0.8 0.9 1 Frequency ratio Bin = mil (1),, Figure 13.7.1 from Dynamics of Structures: Theory and Applications to Earthquake Engineering. by AniE K. Chopra, Prentice-Hall, 2001. Example: A five story shear building m,- = m =100kip3/g ; k,- = k :— 31.54kips/in ; h,- = h =12ft FloorMm SwrySdffness WW ’7‘ W 1 2 —1 1 “1 2 ——1 [M]=m 1 ,[K]=k‘ m1 2 —1 1 —1 2 —1 1 -—1 1 The natural frequencies, modes and modal properties are computed as follows: to; = 0285‘;E ' wg = 0.831 E“ ; wg : 1.310 M ', m m m H: H: w4=1.582 a w5=1.919 if; T; = 2.0860 T2 = 0.6852sec ; T3 = 0.43468ec ; T4 = 0.338388C T5 : 0.29663ec modal vectors 5. 1-078 0.39: 4. 033a Emu ' 3 “m 1.173 2 0.334 i [.173 Db” MaiE ModeS m: = 1.0 P 1 H 1.067 , F2 —0.336 ; “3:017? , F4——0.099 , r15=0.045 Psemlu-vcincily I". inJHcc bx ‘. -\ R5 9 \\ 09.70%? “:33: _ <9 ‘31? ?55 953° :- Q\\ ’2'; B.) ’1 ; OJ "3; ’0 2/ “'3' R; O Q. of? 'l . r\. Fr: ‘3 Y \ «to. \v. I" ,1/ \n? J‘\\ \ ' \x ’/ / Q‘ g" - )2. '3 .— E 1”...“ Pl rupfi. '1! Natural vibration period T». sec aim Using the response spectrum as shown (assume E; :z 5%), the “floor displacements can be computed as: {u}; = 040551); 0.334 1.916 0.641 3.677 I“ {u}: = 1.067 0.695 5.378: 5.139 in. “0'39 TLLSE’L, \ 1.076 6.166 1.173 6.731 . E {f};- = 911M1141141n/Wm114441 0334 4699 0.641 9.401 {f}1 == 1.067(100/g) 0.695 0.13759: 13.141 klps 1“ 1.076 15.617 M09; 1.173 17.211 7‘19"" The results of the peak displacements and static lateral forces per each mode are shown in the figure. Based on the modal responses, the base shear Vb, base moment _ Mb, and the displacement us of the top floor per each mode can be calculated as shown in the figure. (NOTE: Alternatively, one can calculate response such as the base shear and base moment using the general equation: 73- = rfiSufihTz-j.) l 131M13ch ! ib1Moch‘ 1::1Mod33 f1 (kipsl u, [in.) 1'; 11:11:51 “2 tin.) f; (kips: u_11in.1 0.936 12.923 0 239 1 1 17,211 I 6.731 1 20.36:. 5 . 1 1 1 1 I i . i5.8l7q&.136 ; 6.313 3 . I 171 I | : . 13.141 ' —' 5.139 12.114 . '1 0.287 t ' ' '- ! I l l ! / 1 9.401% 3.67.7 '1 22.179 4.399! {I 1.916 E i V“ = I \J ! [Mb] = : Mb; = v1; = 24.333 111135 v1.3 = 9.667-k1ps 51453 = 90.402 kip-fl te)ModeS f5 (kips; us ("111.1 1.14] 0.010 I 3.061 0.026 Ii 4.008 0.034 ‘ 3.634 0.032 2.189 0.019 w v‘ 0.595 ' V 1:5- kip 114,,“ = 20.986 kip-:fi Mb, = 3.716 mm Modal combinations: For example, calculation oi: 1oasersvhear 0 Absolute sum rule: = 60.409 + 24.533 + 9.867 + 2.943 + 0.505 = 98.407kips X273. 1.“ o SquareRoot—Sum—Square (SRSS) rule: _ n SQ {JAKE HAN “'4 V m alga/g,- )2 . Hg Q man: 1 1,171.01: M W _ - M V ‘2' 1:] WI 9/4 {Jam 3 60.4692 + 24.5332 + 9.8672 + 2.9432 + 0.5952 = 66.066kips fljfiigf a Complete Quadratic Combination (CQC)Iru1e: M We) 1 Meg N n '1 [VI/Lflfwb" i 4/1}? Vmaa: ~ 2 z Pij Vbi,ma:s%j,ma:z .‘ WWI-£50717. £31 j=] The calculations of the natural frequency ratio 1613- and the correlation coefi- cients {2,-3- are shown as Natural frequency ratio [3,-3- 321 j=2 j=3 j=4 j=5 1000 0.007 0.003 0.002 0.001 .10.007\10000. 0.044 0.018 0.012 0.003 0.0%..000 0.136 0.002 . 0.002 0.018 0.136‘000000 0.305 0.001 0.012 0.002 0.305x1000 ODE REL. 11,71 6111" 11:. KELWVQLM EMF/UL __./.—-—___-—’-~ m," __ 7—- ' “av-n...“ w Individual V}, term in CQC rule 10.172 601.844 10.687 1.284 3656.476 10.172 1.615 0.306 2575.6 2572.7 2593.2 6.847 ...
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Class25 - Amggmg $13 ._ h _.. m n. __ m _ § {9 Wabbit...

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